A384495 a(n) = Sum_{k=0..n} binomial(n,k)^2 * abs(Stirling1(2*k,k)) * abs(Stirling1(2*n-2*k,n-k)).

1, 2, 26, 648, 25094, 1372100, 99827020, 9233563136, 1045169591270, 140259346792380, 21754963505429340, 3823376222328582480, 749784319125445476092, 162122841942093462239368, 38288723630416561023861048, 9801732906198391239249940800, 2702731846233390353066363949830

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) ~ 2^(4*n - 1/2) * n^(n - 3/2) * w^(2*n) / ((w-1) * Pi^(3/2) * exp(n) * (2*w-1)^n), where w = -LambertW(-1, -exp(-1/2)/2) = 1.7564312086261696769827376166...

Mathematica

Table[Sum[Binomial[n, k]^2 * Abs[StirlingS1[2*k, k]] * Abs[StirlingS1[2*n-2*k, n-k]], {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A187656, A187658, A384496, A384471.

Sequence in context: A302719 A377527 A377547 * A377632 A090247 A371296

Adjacent sequences: A384492 A384493 A384494 * A384496 A384497 A384498

Keyword

nonn

Author

Vaclav Kotesovec, May 31 2025

Status

approved